Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form

IF 2.1 3区 数学 Q1 MATHEMATICS, APPLIED Numerical Methods for Partial Differential Equations Pub Date : 2023-11-27 DOI:10.1002/num.23083
Ruben Caraballo, Chansophea Wathanak In, Alberto F. Martín, Ricardo Ruiz-Baier
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Abstract

In this article, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of parameter-weighted spaces, which allows for a more accurate and robust analysis of the continuous and discrete problems. Furthermore, we conduct a solvability analysis of the proposed method and derive optimal error estimates in appropriate norms. These error estimates are shown to be robust in a variety of regimes, including the case of large Lamé parameters and small permeability and storativity coefficients. To illustrate the effectiveness of the proposed method, we provide a few representative numerical examples, including convergence verification and testing of robustness of block-diagonal preconditioners with respect to model parameters.
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涡量型Biot-Brinkman方程的鲁棒有限元方法及求解方法
在本文中,我们提出了一种新的公式和合适的有限元方法来计算可变形多孔介质中粘性流动的稳态耦合。该方法基于参数加权空间的使用,可以对连续和离散问题进行更准确和鲁棒的分析。此外,我们对所提出的方法进行了可解性分析,并在适当的规范下得出了最优误差估计。这些误差估计在各种情况下都具有鲁棒性,包括在lam参数大、渗透率和存储系数小的情况下。为了说明所提方法的有效性,我们提供了几个有代表性的数值例子,包括收敛性验证和块对角预调节器相对于模型参数的鲁棒性测试。
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来源期刊
CiteScore
7.20
自引率
2.60%
发文量
81
审稿时长
9 months
期刊介绍: An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.
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